Magnetic resonance imaging (MRI) is a well known imaging technique that can be used to observe soft tissues such as the brain, muscles and kidneys. Specific properties of the various compounds found inside tissues, such as water and/or fat, are used to generate images. When subjected to a strong magnetic field, the vector sum of the nuclear magnetic moments of a large number of atoms possessing a nuclear spin angular momentum, such as hydrogen, which is abundant in water and fat, will produce a net magnetic moment in alignment with the externally applied field. The resultant net magnetic moment can furthermore precess with a well-defined frequency that is proportional to the applied magnetic field. After excitation by radio frequency (RF) pulses, relaxation mechanisms bring the net magnetization back to its equilibrium position within a characteristic time T1 (also known as the T1 relaxation time), during which a signal can be detected. The resulting MR image is a complex-valued map of the spatial distribution of the transverse magnetization Mxy in the sample at a specific time point after an excitation.
In MRI, the main magnetic field is produced by a large superconducting electromagnet. Extreme care is taken to ensure that the magnetic field produced by this magnet is uniform. Non-uniformities can result in signal loss, image distortion, image blurring, and poor fat suppression. In MR spectroscopy, field inhomogeneities cause broadening of line-widths and frequency shifts. Due to these problems, great care is taken at the time of installation to ensure that the field produced by the main magnet is extremely uniform; however, when a subject enters the magnetic environment, additional field inhomogeneities are produced due to susceptibility differences between tissues. This problem is enhanced as the main magnetic field is increased. To achieve the stringent field uniformity requirements necessary for MRI, both passive and active magnetic shims are used to ‘fine-tune’ the main field in order to make it as uniform as possible. See, for example, Romeo F., Hoult D. I. Magnet field profiling: analysis and correcting coil design, Magn Reson Med; 1: 44-65 (1984).
Typically, passive shims are utilized to remove inhomogeneities at the time of installation and active room temperature electromagnets are used to mitigate susceptibility induced field deviations. The active magnetic shim coils traditionally consist of gradient coils (discussed in greater detail below) for first-order linear corrections, and an additional set of electromagnets that produce field patterns matching the second-order spherical harmonics. Some high-field systems contain third or even-fourth order shims. Each shim coil must be powered by its own power supply, typically providing up to 10-20 A of current.
Spatial information in MRI, is encoded by linearly varying the main magnetic field using three room temperature electromagnets known as gradient coils. The gradient coils are typically located just inside the “bore” of the main magnet. The gradient coils produce magnetic fields on the order of mT by passing hundreds of amperes of current through their windings. The power required to create these fields is provided by expensive high-performance power amplifiers.
Due to heating and spatial constraints imposed by gradient coil design criteria, the gradient coil fields can contain non-linearities as much as 50% in extreme cases. The non-linearities result in image warping, which must be undone in post-processing of the image. The strength of whole-body gradient systems is in the range of 20-50 mT/m, with specialized systems boasting strengths of 80-100 mT/m and dedicated diffusion systems capable of 300 mT/m. Slew rates for the gradient systems (i.e. how quickly they can be turned on) are around 200 T/m/s; however, due to the onset of peripheral nerve stimulation (PNS) most scanners are operated at slew rates significantly lower than this.
Harris C. T., et al., A New Approach to Shimming: The Dynamically Controlled Adaptive Current Network, Magnetic Resonance Medicine, 71 pp. 859-869 (2014), sets forth a dynamically controlled, active electromagnet that is capable of adaptively changing its wire pattern for the purpose of localized magnetic field shimming. Multiple different spatial profiles can be produced (i.e. both the linear gradients and shim field patterns) using only a single electromagnet powered by a single amplifier, thereby drastically reducing the cost and weight associated with prior art systems. Furthermore, since the adaptive electromagnet can be positioned very close to the patient, lower power is needed for a given field strength, eddy currents induced by switching the magnetic field are reduced if the system is further from the main magnet bore, field inhomogeneities with high spatial frequency can be accounted for, and faster switching without the onset of PNS can be achieved.
A key requirement of the dynamic, adaptive electromagnet set forth in Harris et al. is the ability to represent a continuous current density distribution over a discretized grid of conducting material. However, Harris et al. does not provide any description of how a continuous current density distribution can be transformed into a “discretized” pattern for application to a conducting grid, or any practical implementation of the dynamically controlled adaptive electromagnet.
Additional prior art is relevant to this specification:    Turner R., A target field approach to optimal coil design, J Phys D Appl Phys; 19: L147-L151 (1986).    Yoda K., Analytical design method of self-shielded planar coils. J Appl Phys; 67: 4349-4353 (1990).    Crozier S., Doddrell D. M. Gradient-Coil Design by Simulated Annealing, J Magn Reson Ser A; 103: 354-357(1993).    Lemdiasov R. A., Ludwig R. A Stream Function Method for Gradient Coil Design, Concept Magn Reson B; 26B: 67-80 (2005).    Poole M., Bowtell R. Novel gradient coils designed using the boundary element method, Concept Magn Reson B; 33B: 220-227 (2007).    Poole M., et al. Minimax current density coil design, J Phys D Appl Phys; 43: 095001 (2010).    Juchem C., et al. (2011). Multi-Coil Shimming of the Mouse Brain. Magn Reson Med; 66: 893-900.    Juchem C., et al. (2011). Dynamic Multi-Coil Shimming of the Human Brain at 7 Tesla, J Magn Reson; 212: 280-288.    Harris C. T., et al. Electromagnet design allowing explicit and simultaneous control of minimum wire spacing and field uniformity, Concept Magn Reson B; 41B(4): 120-129 (2012).